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Anisotropic peridynamic model—Formulation and implementation

Division of Mechanics, Department of Mechanical Engineering Lund University, P.O. Box 118, S22100 Lund, Sweden

Special Issues: Peridynamics

In this work, anisotropy is introduced in a peridynamic model. The spherical influence function is replaced by an ellipsoidal influence function. The model is mathematically formulated and implemented into the source files of LAMMPS, extending the program in a straight-forward manner. The extension ca be applied to other peridynamic model and here it is introduced into elastoplastic peridynamic model in LAMMPS. The implemented model is tested through simulating beams loaded in compression. The model is found to alter the material behavior in the simulations compared to the original isotropic mode. A clear qualitative and quantitative difference in behavior is shown independently of pre-existing simulation parameters. The model is shown to be internally consistent. Finally we also demonstrated that the model can easily be extended to include several preferable direction opening for application as modeling elasticplastic deformation of anisotropic heterogeneous crystalline matter.
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1. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range. J Mech Phys Solids 48: 175–209.    

2. Askari E, Bobaru F, Lehoucq RB, et al. (2008) Peridynamics for multiscale materials modeling. J Phys Conf Ser 125: 012078.    

3. Silling SA, Askari E (2005) Meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83: 1526–1535.    

4. Silling SA, Epton M, Weckner O, et al. (2007) Peridynamics States and Constitutive Modeling. J Elasticity 88: 151–184.    

5. Parks ML, Lehoucq RB, Plimpton SJ, et al. (2008) Implementing peridynamics within a molecular dynamics code. Comput Phys Commun 179: 777–783.    

6. Seleson P, Parks ML, Gunzburger M, et al. (2009) Peridynamics as an upscaling of molecular dynamics. Multiscale Model Sim 8: 204–227.    

7. LAMMPS, Available from: http://lammps.sandia.gov.

8. Parks ML, Seleson P, Plimpton SJ, et al. (2011) Peridynamics with LAMMPS: A User Guide v0.3 Beta. Sandia National Laboratories.

9. Mitchell J (2011) A nonlocal ordinary state-based plasticity model for peridynamics. Sandia National Lab Report.

10. Mitchell J (2011) A non-local, ordinary-state-based viscoelasticity model for peridynamics. Sandia National Lab Report.

11. Rahman R, Foster JT (2014) Implementation of elastic–plastic model in LAMMPS. University of Texas at San Antonio, Sandia National Laboratory.

12. Rahman R, Foster JT (2014) Implementation of linear viscoelasticity model in pdlammps. University of Texas at San Antonio, Sandia National Laboratory.

13. Rahman R, Foster JT, Plimpton SJ (2014) PDLAMMPS-made easy. University of Texas at San Antonio, Sandia National Laboratory.

14. Lehoucq RB, Silling SA (2008) Force flux and the peridynamic stress tensor. J Mech Phys Solids 56: 1566–1577.    

15. Seleson P, Parks ML (2012) On the role of the influence function in the peridynamic theory. University of Texas at San Antonio, Sandia National Laboratory.

16. Trefethen LN, Bau III D (1997) Numerical Linear Algebra.

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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